Abstract : Kummerfourfolds, a generalization of K3 surfaces (and, in some sense, of abelian surfaces), belong to the class of Hyperk¨ahler manifolds, which exhibit rich but intricate geometry. In this talk, we explore the projective duality of certain special Kummer fourfolds and explain how O'Grady's theory of theta groups can be used to derive their equations. This work, carried out in collaboration with Agostini, Beri, and Rios-Ortiz, contributes to a broader framework of classical results involving moduli spaces of sheaves on curves and embeddings of abelian surfaces.

Keywords : hyperkähler manifolds; projective duality; Kummer